Dealing with Null values in Differenced Data

Hi everyone,

I'm running a regression analysis to try and explain the effect of advertising on brand interest. Essentially, what I want to be able to say is "an x% change in advertising spend drives a y% change in brand interest".

My problem is that I have a lot of data points where advertising was not run - e.g. zero values for the spend variable in my spreadsheet - so I can't calculate the % change for those periods since I get "divide by zero" errors; hence I can't run the regression.

Can someone suggest what's the best way to deal with this from either theory or past experience? E.g. do I simply replace the divide-by-zero errors with 0 or something, or is there another approach?

I thought about just doing a simplistic two-sample difference of means test to compare the "light" and "dark" periods of advertising, but this won't work since the advertiser had ads "on" most of the time, and would switch off for a few weeks at a time before ramping up again. Plus I need to take spend of a few different variables into account so the way I see it regression is my only way.

Any suggestions are much appreciated.